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<p>In this research work quantum neural network using simple harmonic oscillator perturbed by an electric field is proposed. This work demonstrated that it is possible to generate a time varying wave function in Schrodinger’s equation by controlling the electric field applied to a quantum harmonic oscillator, whose modulus square tracks a given probability density function (PDF). The adaptation scheme for the control electric field is generated via stochastic gradient algorithm. Statistical performance analysis of the algorithm is carried out using perturbation theory, i.e. by evaluating the shift in the control electric field under small perturbations of the PDF to be tracked. In addition “Fine tuning of converged electric field using large deviation principle (LDP)", “ State variable form of the truncated Schrodinger equation" and “ Dynamics of the electric field weight in terms of the state variable co-efficient vector" are also analysed. This work has application in data compression, PDF synthesis (for example synthesis of Electroencephalogram (EEG) PDF from speech PDF and visa versa)</p>

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Dynamic estimation of probability density using quantum neural network based on simple harmonic oscillator perturbed by an electric field

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • Guguloth Sagar,
  • Harish Parthasarathy,
  • Vijyant Agarwal

摘要

In this research work quantum neural network using simple harmonic oscillator perturbed by an electric field is proposed. This work demonstrated that it is possible to generate a time varying wave function in Schrodinger’s equation by controlling the electric field applied to a quantum harmonic oscillator, whose modulus square tracks a given probability density function (PDF). The adaptation scheme for the control electric field is generated via stochastic gradient algorithm. Statistical performance analysis of the algorithm is carried out using perturbation theory, i.e. by evaluating the shift in the control electric field under small perturbations of the PDF to be tracked. In addition “Fine tuning of converged electric field using large deviation principle (LDP)", “ State variable form of the truncated Schrodinger equation" and “ Dynamics of the electric field weight in terms of the state variable co-efficient vector" are also analysed. This work has application in data compression, PDF synthesis (for example synthesis of Electroencephalogram (EEG) PDF from speech PDF and visa versa)